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DOE OSTI2025

High-resolution tunnelling spectroscopy of fractional quantum Hall states

Strong interactions between electrons in two-dimensional systems in the presence of a high magnetic field give rise to fractional quantum Hall states that host quasiparticles with a fractional charge and fractional exchange statistics. Here, in this work, we demonstrate high-resolution scanning tunnelling microscopy and spectroscopy of fractional quantum Hall states in ultra-clean Bernal-stacked bilayer graphene devices. Spectroscopy measurements show sharp excitations that have been predicted to emerge when electrons fractionalize into bound states of quasiparticles. We found energy gaps for candidate non-abelian fractional states that are larger by a factor of five than those in other related systems, for example, semiconductor heterostructures, and this suggests that bilayer graphene is an ideal platform for manipulating these quasiparticles and for creating topological quantum bits. We also found previously unobserved fractional states in our very clean graphene samples.

quantum Hall↗

DOE OSTI2025

Microscopic signatures of topology in twisted MoTe 2

In moiré materials with flat electronic bands and suitable quantum geometry, strong correlations can give rise to various topological states of matter. The non-trivial band topology of twisted MoTe 2 , which is responsible for its fractional quantum anomalous Hall states, is predicted to arise from a skyrmion lattice texture in the layer pseudospin of the electronic wavefunctions. Tracing the layer polarization of wavefunctions within the moiré unit cell can, thus, offer insights into the band topology. Here we measure the out-of-plane component of the layer-pseudospin skyrmion textures of twisted MoTe 2 using scanning tunnelling microscopy and spectroscopy. We do this by simultaneously visualizing the moiré lattice structure and the spatial localization of its electronic states. We find that the wavefunctions associated with the topological flat bands exhibit a spatially dependent layer polarization within the moiré unit cell, in agreement with our theoretical modelling. Furthermore, our work enables future local probe studies of the intertwined correlated and topological states arising in gate-tunable devices.

Electronic properties and materials↗

DOE OSTI2025

Topological excitonic insulator with tunable momentum order

Correlated topological materials often maintain a delicate balance among physical symmetries. Many topological orders are symmetry protected, whereas most correlated phenomena arise from spontaneous symmetry breaking. Cases where symmetry breaking induces a non-trivial topological phase are rare. Here we demonstrate the presence of two such phases in Ta 2 Pd 3 Te 5 , where Coulomb interactions form excitons that condense below 100 K, one with zero and the other with finite momentum. We observed a full spectral bulk gap, which stems from exciton condensation. This topological excitonic insulator state spontaneously breaks mirror symmetries but involves a weak structural coupling. Scanning tunnelling microscopy shows gapless boundary modes in the bulk insulating phase. Their magnetic field response, together with theoretical modelling, indicates a topological origin. These observations establish Ta 2 Pd 3 Te 5 as a topological excitonic insulator in a three-dimensional crystal. Finally, our results manifest a unique sequence of topological exciton condensations in a bulk crystal, offering exciting opportunities to study critical behaviour and excitations.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Frieze charge-stripes in a correlated kagome superconductor

In kagome metals, geometric frustration, electronic correlations and band topology combine to produce a wide range of intriguing phenomena. Among them, CsCr$_3$Sb$_5$ offers an opportunity to investigate unconventional superconductivity in a strongly correlated kagome system, with indications of frustrated magnetism and quantum criticality. Here, we demonstrate a cascade of density-wave transitions with distinct symmetries in bulk single crystals of CsCr$_3$Sb$_5$. Using spectroscopic imaging scanning tunneling microscopy, we uncover a unidirectional density wave that breaks all mirror symmetries -- resembling a chiral density wave -- but that also retains a mirror glide symmetry. We refer to this as a frieze charge stripe order phase, as its symmetry properties correspond to one of the fundamental frieze symmetry groups. A combination of high-resolution imaging, Fourier analysis and theoretical simulations reveal the key role of sublattice degrees of freedom in stabilizing this phase, characterized by internal chiral textures of opposite handedness. These findings suggest that superconductivity in CsCr$_3$Sb$_5$ emerges from this distinct density wave state and provide fresh insight into realizing electronic phases governed by frieze symmetry groups in quantum materials.

Cheng, Siyu [Boston College, Chestnut Hill, MA (Un↗

DOE OSTI2021

Giant nonlinear optical responses from photon-avalanching nanoparticles

Avalanche phenomena use steeply nonlinear dynamics to generate disproportionately large responses from small perturbations, and are found in a multitude of events and materials. Photon avalanching enables technologies such as optical phase-conjugate imaging, infrared quantum counting and efficient upconverted lasing. However, the photon-avalanching mechanism underlying these optical applications has been observed only in bulk materials and aggregates, limiting its utility and impact. In this study we report the realization of photon avalanching at room temperature in single nanostructures-small, Tm 3+ -doped upconverting nanocrystals-and demonstrate their use in super-resolution imaging in near-infrared spectral windows of maximal biological transparency. Avalanching nanoparticles (ANPs) can be pumped by continuous-wave lasers, and exhibit all of the defining features of photon avalanching, including clear excitation-power thresholds, exceptionally long rise time at threshold, and a dominant excited-state absorption that is more than 10,000 times larger than ground-state absorption. Beyond the avalanching threshold, ANP emission scales nonlinearly with the 26th power of the pump intensity, owing to induced positive optical feedback in each nanocrystal. This enables the experimental realization of photon-avalanche single-beam super-resolution imaging with sub-70-nanometre spatial resolution, achieved by using only simple scanning confocal microscopy and without any computational analysis. Pairing their steep nonlinearity with existing super-resolution techniques and computational methods, ANPs enable imaging with higher resolution and at excitation intensities about 100 times lower than other probes. The low photon-avalanching threshold and excellent photostability of ANPs also suggest their utility in a diverse array of applications, including sub-wavelength imaging and optical and environmental sensing.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Cascade of electronic transitions in magic-angle twisted bilayer graphene

Magic-angle twisted bilayer graphene exhibits a variety of electronic states, including correlated insulators, superconductors and topological phases. Understanding the microscopic mechanisms responsible for these phases requires determination of the interplay between electron–electron interactions and quantum degeneracy (the latter is due to spin and valley degrees of freedom). Signatures of strong electron–electron correlations have been observed at partial fillings of the flat electronic bands in recent spectroscopic measurements, and transport experiments have shown changes in the Landau level degeneracy at fillings corresponding to an integer number of electrons per moiré unit cell. However, the interplay between interaction effects and the degeneracy of the system is currently unclear. Here in this paper we report a cascade of transitions in the spectroscopic properties of magic-angle twisted bilayer graphene as a function of electron filling, determined using high-resolution scanning tunnelling microscopy. We find distinct changes in the chemical potential and a rearrangement of the low-energy excitations at each integer filling of the moiré flat bands. These spectroscopic features are a direct consequence of Coulomb interactions, which split the degenerate flat bands into Hubbard sub-bands. We find these interactions, the strength of which we can extract experimentally, to be surprisingly sensitive to the presence of a perpendicular magnetic field, which strongly modifies the spectroscopic transitions. The cascade of transitions that we report here characterizes the correlated high-temperature parent phase from which various insulating and superconducting ground-state phases emerge at low temperatures in magic-angle twisted bilayer graphene.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Detection of a pair density wave state in UTe2

Abstract Spin-triplet topological superconductors should exhibit many unprecedented electronic properties, including fractionalized electronic states relevant to quantum information processing. Although UTe 2 may embody such bulk topological superconductivity 1–11 , its superconductive order parameter Δ( k ) remains unknown 12 . Many diverse forms for Δ( k ) are physically possible 12 in such heavy fermion materials 13 . Moreover, intertwined 14,15 density waves of spin (SDW), charge (CDW) and pair (PDW) may interpose, with the latter exhibiting spatially modulating 14,15 superconductive order parameter Δ( r ), electron-pair density 16–19 and pairing energy gap 17,20–23 . Hence, the newly discovered CDW state 24 in UTe 2 motivates the prospect that a PDW state may exist in this material 24,25 . To search for it, we visualize the pairing energy gap with μeV-scale energy resolution using superconductive scanning tunnelling microscopy (STM) tips 26–31 . We detect three PDWs, each with peak-to-peak gap modulations of around 10 μeV and at incommensurate wavevectors P i =1,2,3 that are indistinguishable from the wavevectors Q i =1,2,3 of the prevenient 24 CDW. Concurrent visualization of the UTe 2 superconductive PDWs and the non-superconductive CDWs shows that every P i : Q i pair exhibits a relative spatial phase δϕ ≈ π. From these observations, and given UTe 2 as a spin-triplet superconductor 12 , this PDW state should be a spin-triplet PDW 24,25 . Although such states do exist 32 in superfluid 3 He, for superconductors, they are unprecedented.

Science & Technology - Other Topics↗

DOE OSTI2023

Smectic pair-density-wave order in EuRbFe 4 As 4

The pair density wave (PDW) is a superconducting state in which Cooper pairs carry centre-of-mass momentum in equilibrium, leading to the breaking of translational symmetry. Experimental evidence for such a state exists in high magnetic field and in some materials that feature density-wave orders that explicitly break translational symmetry. However, evidence for a zero-field PDW state that exists independent of other spatially ordered states has so far been elusive. Here we show that such a state exists in the iron pnictide superconductor EuRbFe 4 As 4 , a material that features co-existing superconductivity (superconducting transition temperature ( T c ) ≈ 37 kelvin) and magnetism (magnetic transition temperature ( T m ) ≈ 15 kelvin). Using spectroscopic imaging scanning tunnelling microscopy (SI-STM) measurements, we show that the superconducting gap at low temperature has long-range, unidirectional spatial modulations with an incommensurate period of about eight unit cells. Upon increasing the temperature above Tm, the modulated superconductor disappears, but a uniform superconducting gap survives to T c . When an external magnetic field is applied, gap modulations disappear inside the vortex halo. The SI-STM and bulk measurements show the absence of other density-wave orders, indicating that the PDW state is a primary, zero-field superconducting state in this compound. FInally, both four-fold rotational symmetry and translation symmetry are recovered above T m , indicating that the PDW is a smectic order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Quantum textures of the many-body wavefunctions in magic-angle graphene

Interactions among electrons create novel many-body quantum phases of matter with wavefunctions that often reflect electronic correlation effects, broken symmetries, and novel collective excitations. A wide range of quantum phases has been discovered in MATBG, including correlated insulating, unconventional superconducting, and magnetic topological phases. The lack of microscopic information, including precise knowledge of possible broken symmetries, has thus far hampered our understanding of MATBG's correlated phases. Here we use high-resolution scanning tunneling microscopy to directly probe the wavefunctions of the correlated phases in MATBG. The squares of the wavefunctions of gapped phases, including those of the correlated insulators, pseudogap, and superconducting phases, show distinct patterns of broken symmetry with a √3 x √3 super-periodicity on the graphene atomic lattice that has a complex spatial dependence on the moiré superlattice scale. We introduce a symmetry-based analysis to describe our measurements of the wavefunctions of MATBG's correlated phases with a set of complex-valued local order parameters. For the correlated insulators in MATBG, at fillings of ±2 electrons per moiré unit cell relative to charge neutrality, we compare the observed quantum textures to those expected for proposed theoretical ground states. In typical MATBG devices, the textures of correlated insulators' wavefunctions closely match those of the theoretically proposed IKS order, while in ultra-low-strain samples our data has local symmetries like those of a T-IVC phase. Here, we also study the wavefunction of MATBG's superconducting state, revealing strong signatures of intervalley coherence that can only be distinguished from those of the insulator with our phase-sensitive measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Cooper-pair density modulation state in an iron-based superconductor

Superconducting (SC) states that break space-group symmetries of the underlying crystal can exhibit nontrivial spatial modulation of the order parameter. Previously, such states were intimately associated with the breaking of translational symmetry, resulting in the density-wave orders, with wavelengths spanning several unit cells. However, a related basic concept has long been overlooked: when only intra-unit-cell symmetries of the space group are broken, the SC states can show a distinct type of nontrivial modulation preserving long-range lattice translation. Here, in this study, we refer to this new concept as the pair density modulation (PDM) and report the first observation of a PDM state in exfoliated thin flakes of the iron-based superconductor FeTe 0.55 Se 0.45 . Using scanning tunnelling microscopy (STM), we discover robust SC gap modulation with the wavelength corresponding to the lattice periodicity and the amplitude exceeding 30% of the gap average. Notably, we find that the observed modulation originates from the large difference in SC gaps on the two nominally equivalent iron sublattices. The experimental findings, backed up by model calculations, suggest that, in contrast to the density-wave orders, the PDM state is driven by the interplay of sublattice symmetry breaking and a peculiar nematic distortion specific to the thin flakes. Our results establish new frontiers for exploring the intertwined orders in strong-correlated electronic systems and open a new chapter for iron-based superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Visualizing interaction-driven restructuring of quantum Hall edge states

Many topological phases host gapless boundary modes that can be dramatically modified by electronic interactions. Even for the long-studied edge modes of quantum Hall phases, forming at the boundaries of two-dimensional (2D) electron systems, the nature of such interaction-induced changes has been elusive. Despite advances made using local probes, key experimental challenges persist: the lack of direct information about the internal structure of edge states on microscopic scales, and complications from edge disorder. Here, we use scanning tunneling microscopy (STM) to image pristine electrostatically defined quantum Hall edge states in graphene with high spatial resolution and demonstrate how correlations dictate the structures of edge channels on both magnetic and atomic length scales. For integer quantum Hall states in the zeroth Landau level, we show that interactions renormalize the edge velocity, dictate the spatial profile for copropagating modes, and induce unexpected edge valley polarization that differ from those of the bulk. While some of our findings can be understood by mean-field theory, others show breakdown of this picture, highlighting the roles of edge fluctuations and inter-channel couplings. We also extend our measurements to spatially resolve the edge state of fractional quantum Hall phases and detect spectroscopic signatures of interactions in this chiral Luttinger liquid. Furthermore, our study establishes STM as a promising tool for exploring edge physics of the rapidly expanding 2D topological phases, including newly realized fractional Chern insulators.

Electronic properties and materials↗

DOE OSTI2026

Limitations of probing field-induced response with STM

The kagome superconductors AV 3 Sb 5 (where A = K, Cs, Rb) exhibit intertwined density waves, unconventional superconductivity and time-reversal symmetry breaking without spin magnetism, with scanning tunnelling microscopy (STM) studies reporting, albeit not universally, magnetic-field-dependent changes in the apparent chirality of the 2 × 2 charge density wave (CDW). Related to this, Xing et al. investigated the effects of magnetic and electric fields on the 2 × 2 CDW state and the lattice structure of kagome superconductor RbV3Sb5, reporting a field-induced ~1% change in the in-plane lattice constants, concomitant with the CDW intensity modification, controlled by the field direction. Here we demonstrate how the apparent magnetic field induced lattice and CDW intensity change can be explained as a consequence of two independent experimental artifacts: a reconfiguration of atoms at the STM tip apex that alters the amplitudes of CDW modulations, and piezo creep, hysteresis and thermal drift, which artificially distort STM topographs. Here, we argue that the reported piezomagnetism could be attributed to experimental artifacts rather than an intrinsic magnetic-field-induced change of the sample.

Candelora, Christopher [Boston College, Chestnut H↗

DOE OSTI2026

Visualizing the impact of quenched disorder on 2D electron Wigner solids

Electron Wigner solids (WSs) provide an ideal system for understanding the competing effects of electron–electron and electron–disorder interactions, a central unsolved problem in condensed matter physics. Progress in this topic has been limited by a lack of single-defect-resolved experimental measurements as well as accurate theoretical tools to enable realistic experiment/theory comparison. Here, in this study, we overcome these limitations by combining atomically resolved scanning tunnelling microscopy (STM) with neural-quantum-state quantum Monte Carlo (NQS-QMC) simulation of disordered 2D electron WSs to discover new disorder-induced physical regimes of correlated electron behaviour. STM was used to image the electron density (n e )-dependent evolution of electron WSs in gate-tunable bilayer MoSe 2 (BL-MoSe 2 ) devices with varying long-range (n LR ) and short-range (n SR ) disorder densities. These images were compared with NQS-QMC simulations using realistic disorder maps extracted from experiment, thus allowing the roles of different disorder types to be disentangled. We identify two distinct physical regimes for disordered electron WSs that depend on n SR . For n SR ≲ n e , the WS behaviour is dominated by long-range disorder and features extensive mixed solid–liquid phases, a new type of local re-entrant melting/crystallization and prominent Friedel oscillations. By contrast, when n SR ≫ n e , these features are suppressed and a more robust amorphous WS phase emerges that persists to higher n e , highlighting the importance of short-range disorder in this regime. Our work establishes a powerful framework for studying disordered quantum solids through a combined experimental–theoretical approach.

Ge, Zhehao [University of California, Berkeley, CA↗

DOE OSTI2020

Nanofabrication of synthetic nanoporous geomaterials: from nanoscale-resolution 3D imaging to nano-3D-printed digital (shale) rock

Abstract Advances in imaging have made it possible to view nanometer and sub-nanometer structures that are either synthesized or that occur naturally. It is believed that fluid dynamic and thermodynamic behavior differ significantly at these scales from the bulk. From a materials perspective, it is important to be able to create complex structures at the nanometer scale, reproducibly, so that the fluid behavior may be studied. New advances in nanoscale-resolution 3D-printing offer opportunities to achieve this goal. In particular, additive manufacturing with two-photon polymerization allows creation of intricate structures. Using this technology, a creation of the first nano-3D-printed digital (shale) rock is reported. In this paper, focused ion beam-scanning electron microscopy (FIB-SEM) nano-tomography image dataset was used to reconstruct a high-resolution digital rock 3D model of a Marcellus Shale rock sample. Porosity of this 3D model has been characterized and its connected/effective pore system has been extracted and nano-3D-printed. The workflow of creating this novel nano-3D-printed digital rock 3D model is described in this paper.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

2D-to-3D image translation of complex nanoporous volumes using generative networks

Image-based characterization offers a powerful approach to studying geological porous media at the nanoscale and images are critical to understanding reactive transport mechanisms in reservoirs relevant to energy and sustainability technologies such as carbon sequestration, subsurface hydrogen storage, and natural gas recovery. Nanoimaging presents a trade off, however, between higher-contrast sample-destructive and lower-contrast sample-preserving imaging modalities. Furthermore, high-contrast imaging modalities often acquire only 2D images, while 3D volumes are needed to characterize fully a source rock sample. In this work, we present deep learning image translation models to predict high-contrast focused ion beam-scanning electron microscopy (FIB-SEM) image volumes from transmission X-ray microscopy (TXM) images when only 2D paired training data is available. We introduce a regularization method for improving 3D volume generation from 2D-to-2D deep learning image models and apply this approach to translate 3D TXM volumes to FIB-SEM fidelity. We then segment a predicted FIB-SEM volume into a flow simulation domain and calculate the sample apparent permeability using a lattice Boltzmann method (LBM) technique. Results show that our image translation approach produces simulation domains suitable for flow visualization and allows for accurate characterization of petrophysical properties from non-destructive imaging data.

58 GEOSCIENCES↗

DOE OSTI2022

Visualizing the unusual spectral weight transfer in DyBa2Cu3O7–δ thin film

Abstract We report a Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM) study of a DyBa 2 Cu 3 O 7-δ (DBCO) thin film ( T c ~ 79 K) synthesized by the molecular beam epitaxy (MBE). We observed an unusual transfer of spectral weight in the local density of states (LDOS) spectra occurring only within the superconducting gap. By a systematic control of the tip-sample distance and the junction resistance, we demonstrate that the spectral weight transfer can be switched at a nano-meter length scale. These results suggest that an interaction between the STM tip and the sample alters the electronic configurations in the film. This probably originates from a combination of an intrinsic band bending at the interface between the surface and the bulk, and a tip-induced band bending. These results may open a new avenue for band engineering and applications of thin films of high- T c cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Complex magnetic properties associated with competing local and itinerant magnetism in ${\text {Pr}}_2 {\text {Co}}_{0.86} {\text {Si}}_{2.88}$

Ternary intermetallic compound ${\text {Pr}}_2 {\text {Co}}_{0.86} {\text {Si}}_{2.88}$ has been synthesized in single phase and characterized by x-ray diffraction, scanning electron microscopy with energy dispersive x-ray spectroscopy (SEM-EDX) analysis, magnetization, heat capacity, neutron diffraction and muon spin rotation/relaxation ( $\mu$ SR) measurements. The polycrystalline compound was synthesized in single phase by introducing necessary vacancies in Co/Si sites. Magnetic, heat capacity, and zero-field neutron diffraction studies reveal that the system undergoes magnetic transition below $\sim$ 4 K. Neutron diffraction measurement further reveals that the magnetic ordering is antiferromagnetic in nature with an weak ordered moment. The high temperature magnetic phase has been attributed to glassy in nature consisting of ferromagnetic clusters of itinerant (3 d ) Co moments as evident by the development of internal field in zero-field $\mu$ SR below 50 K. The density-functional theory (DFT) calculations suggest that the low temperature magnetic transition is associated with antiferromagnetic coupling between Pr 4 f and Co 3 d spins. Pr moments show spin fluctuation along with unconventional orbital moment quenching due to crystal field. The evolution of the symmetry and the crystalline electric field environment of Pr-ions are also studied and compared theoretically between the elemental Pr and when it is coupled with other elements such as Co. The localized moment of Pr 4 f and itinerant moment of Co 3 d compete with each other below $\sim$ 20 K resulting in an unusual temperature dependence of magnetic coercivity in the system.

36 MATERIALS SCIENCE↗

DOE OSTI2021

A multi-technique approach to understanding delithiation damage in LiCoO2 thin films

Abstract We report on the delithiation of LiCoO 2 thin films using oxalic acid (C 2 H 2 O 4 ) with the goal of understanding the structural degradation of an insertion oxide associated with Li chemical extraction. Using a multi-technique approach that includes synchrotron radiation X-ray diffraction, scanning electron microscopy, micro Raman spectroscopy, photoelectron spectroscopy and conductive atomic force microscopy we reveal the balance between selective Li extraction and structural damage. We identify three different delithiation regimes, related to surface processes, bulk delithiation and damage generation. We find that only a fraction of the grains is affected by the delithiation process, which may create local inhomogeneities. However, the bulk delithiation regime is effective to delithiate the LCO film. All experimental evidence collected indicates that the delithiation process in this regime mimics the behavior of LCO upon electrochemical delithiation. We discard the formation of Co oxalate during the chemical extraction process. In conclusion, the chemical route to Li extraction provides additional opportunities to investigate delithiation while avoiding the complications associated with electrolyte breakdown and simplifying in-situ measurements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗